The sorting algorithm assumes that the integers to be sorted tend to have an uniform distribution, which is the key to the performance of this algorithm. For example, if \(n\)  integers are sorted exactly into \(n\)  buckets, the running time is \(\Theta (n)\) . If the integers are not uniformly distributed, the algorithm may still run in linear time if the sum of the squares of the bucket sizes is linear in the total number of elements [1]}.
